Passive molecular movements in cells are often claimed to exhibit ``anomalous subdiffusion'', where the mean-squared displacement (MSD) scales as a power law of time with exponent $\alpha< 1$. Diffusion hindrance by obstacles is often invoked to explain these observations. In many studies of hindered diffusion, the estimated values of $\alpha$ vary strongly. This led to the hypothesis that $\alpha$ depends on obstacle density. This is however at odds with the theoretical support for hindered diffusion among randomly located immobile obstacles, which predicts that true subdiffusion occurs only in the vicinity of the threshold for the percolation of obstacles, and that $\alpha$ takes a {\it unique}, universal value. Here, we present refined simulations of hindered diffusion with biologically realistic parameters and bring forth four main contributions. ({\it i}) We confirm that diffusion hindered by randomly located immobile obstacles does not exhibit variations of $\alpha$ and ({\it ii}) that the MSD in fact never scales like a power law of time. ({\it iii}) In contrast to diffusing obstacles, obstacles fluctuating around equilibrium positions preserve and even emphasize anomalous regimes. ({\it iv}) Hindered diffusion is not equivalent to anomalous diffusion due to random traps with heavy-tailed trap time distribution. These results shed new light on the existing literature about subdiffusion.